First slide

Introduction to real valued functions

Question

If function $f$ and $g$ given by $f (x) = \log (x - 1) - \log (x - 2)$ and $g (x) = \log (\frac{x - 1}{x - 2})$ are equal then x lies in the interval

Moderate

A

$[1, 2]$
B

$[1, 2)$
C

$(2, \infty)$
D

$[- \infty, \infty]$

Solution

$f (x)$ is defined for all x satisfying
$x - 1 > 0$ and $x - 2 > 0 i.e. x > 2$
Domain $(f) = (2, \infty) . . . . . . . (i)$
$g (x)$ is defined for all x satisfying
$\frac{x - 1}{x - 2} > 0 \Rightarrow x \in (- \infty, 1) \cup (2, \infty)$
Domain $(g) = (- \infty, 1) \cup (2, \infty)$ ……….(ii)
Thus $f (x)$ and $g (x)$ are equal for all x belonging to their
common domain i.e $(2, \infty)$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App